Extracting Meaningful Curves from Images

Since the beginning, Mathematical Morphology has proposed to extract shapesfrom images as connected components of level sets. These methods have proved veryefficient in shape recognition and shape analysis. In this paper, we present an improved method to select the most meaningful level lines (boundaries of level sets) from an image. This extraction can be based on statistical arguments, leading to a parameter free algorithm. It permits to roughly extract all pieces of level lines of an image, that coincide with pieces of edges. By this method, the numberof encoded level lines is reduced by a factor 100, without any loss of shape contents. In contrast to edge detection algorithms or snakes methods, such a level lines selection method delivers accurate shape elements, without user parameter since selection parameters can be computed by the Helmholtz Principle. The paper aims at improving the original method proposed in [10]. We give a mathematicalinterpretation of the model, which explains why some pieces of curve are overdetected. We introduce a multiscale approach that makes the method more robust to noise. A more local algorithm is introduced, taking local contrast variations into account. Finally, we empirically prove that regularity makes detection more robust but does not qualitatively change the results.Frédéric Cao graduated from the École Polytechnique (France), and obtained his Ph.D. in 2000 at École Normale Supérieure de Cachan. From 2001, he has been with Irisa (Inria Rennes). His research interests are still image and video analysis by geometrical methods, including partial differential equations and statistical methods.Pablo Musé was born in Montevideo, Uruguay, in 1975. He received the Electrical Engineer degree from the Universidad de la Repblica, Uruguay, in 1999, and the DEA (M.Sc.) in Mathematics, Vision and Learning from the École Normale Supérieure de Cachan, France, in 2001. He has obtained a Ph.D. in Applied Mathematics in 2004 in ENS Cachan, where he currently has a researcher position.Frédéric Sur was born in 1976. He studied mathematics at École Normale Supérieure de Cachan from 1997 to 2001 and received the DEA Mathématiques, Vision, Apprentissage. He obtained his Ph.D. thesis in 2004 and now he has a post doc position in LORIA/CNRS.